X-ray tomographic imaging, in its simplest expression, is an X-ray beam traversing an object, and a detector relating the overall attenuation per ray. The attenuation is derived from a comparison of the same ray with and without the presence of the object. From this conceptual definition, several steps are required to properly construct/reconstruct an image. For instance, the finite size of the X-ray generator, the nature and shape of the filter blocking the very low energy X-rays from the generator, the details of the geometry and characteristics of the detector, and the capacity of the acquisition system are all elements that affect how reconstruction is performed.
In one of many possible geometries, an X-ray source on top of the graph shown in FIG. 1 is emitting an X-ray beam forming a fan or cone, traversing the object. While a wide range of values can exist, typically, the distance “C” is around 100 cm, “B” is around 60 cm, and “A” is around 40 cm. In tomography, each point of the object can be traversed by a collection of rays covering at least 180 degrees. Thus, the entire X-ray generator and detector assembly can rotate around the patient. Mathematical considerations show that tomographic conditions are met when a scan of 180 degrees plus a fan angle is performed.
Statistical weighting is an important component in CT iterative reconstruction algorithms. In conventional systems, it is generally believed that the statistical weighting scheme should be the count information recorded by the detector, which is governed by a Poisson stochastic process, e.g., directly using count information as weights. However, as shown in FIGS. 2A (filtered back-projection) and 2B (iterative reconstruction), due to strong count weighting, reconstructed images suffer from artifacts and have poor image quality.